Theorems · Theorem · general topology
nhdsWithin_le_iff
∀ {α : Type u_1} [inst : TopologicalSpace α] {s t : Set α} {x : α}, nhdsWithin x s ≤ nhdsWithin x t ↔ t ∈ nhdsWithin x s- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- nhdsWithinstatement · cited by 1,912
- Filter.set_eventuallyLE_iff_mem_inf_principalproof · cited by 2
- Filter.set_eventuallyLE_iff_inf_principal_leproof · cited by 1
Cited by10
Results whose statement or proof uses this declaration.
- nhdsWithin_le_of_memproof · cited by 8
- HasFDerivWithinAt.mono_of_mem_nhdsWithinproof · cited by 6
- hasDerivWithinAt_taylorWithinEvalproof · cited by 2
- tangentConeAt_mono_nhdsproof · cited by 2
- VectorField.eventually_contMDiffWithinAt_mpullbackWithin_extChartAt_symmproof · cited by 2
- Real.ContinuousOn.eq_of_eqOn_Iooproof · cited by 2
- UniqueMDiffWithinAt.mono_of_mem_nhdsWithinproof · cited by 2
- Complex.nhdsWithin_stolzCone_le_nhdsWithin_stolzSetproof · cited by 1
- fderivWithin_fderivWithin_eq_of_mem_nhdsWithinproof · cited by 1
- ContDiffWithinAt.hasFDerivWithinAt_nhdsproof · cited by 1